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where <math>\mathbf{x}_0\equiv\mathbf{x}</math>, and the <math>\mathbf{x}_i</math> for <math>i>0</math> are given by {{EquationNote|1|Eq. 1}}. The solution of the optimal control problem is the minimizing control sequence
<math>\mathbf{U}^*(\mathbf{x})\equiv \operatorname{argmin}_{\mathbf{U}} J_0(\mathbf{x},\mathbf{U}).</math>
''Trajectory optimization'' means finding <math>\mathbf{U}^*(\mathbf{x})</math> for a particular <math>\mathbf{x}_0</math>, rather than for all possible initial states.
== Dynamic programming ==
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